While not technically brain dead (as far as I've read online), Alfie has a progressive, fatal neurodegenerative disease that has killed off most of his brain tissue. Even in the unlikely event that he survives his infections and disease progression halts, all of that damage is permanent and he has zero chance of living life in any kind of non-vegetative fashion.
It is morally objectionable to sustain a human being in this state - the life support should have been withdrawn far earlier.